ITEC 1010 Study Guide - Final Guide: Confidence Interval, Test Statistic
13 Aug 2020
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Discuss the problem of finding a confidence interval for the difference μ1−μ2between the two
means of two normal distributions if the variances and areknown but not necessarily equal.
Step-1
Let and be independent random samples from and respectively. Let and are the means of random samples. Assume that the population
variances are known.
Step-2
Consider an estimate, for the difference of two means
The expected value of is calculated as follows:
The variance of is calculated as follows:
Step-3
We have that the difference of two means are approximately normal distributed, that’s
Thus, the standard test statistic for the difference of means is defined as follows:
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